Timeline for About reflections of reflection groups

7 events

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Dec 23, 2016 at 18:25	comment	added	Sam Hopkins		This homework solution sheet seems to provide such an argument: math.sfsu.edu/federico/Clase/Coxeter/HomeworkSolutions/9.pdf
Dec 23, 2016 at 18:21	comment	added	Sam Hopkins		And by the way, I think it requires at least a small argument to show that every reflection has a reduced word that is a palindrome.
Dec 23, 2016 at 18:20	comment	added	Sam Hopkins		In the theory of abstract Coxeter groups, "reflections" are usually defined to be the elements in the set $\{wsw^{-1}\colon w \in W, s\in S\}$ (where $(W,S)$ is some Coxeter system). Thus, reflections across codimension $>1$ subspaces are not usually called reflections in this context.
Dec 23, 2016 at 14:18	vote	accept	bing
Dec 23, 2016 at 14:16	vote	accept	bing
Dec 23, 2016 at 14:17
Dec 21, 2016 at 16:35	comment	added	Steven Stadnicki		A specific example (in $\mathbb{R}^3$) of an element of determinant $-1$ that's not a reflection is the composition of a reflection in the $xy$ plane with a rotation of $\frac{2\pi}n$ about the $z$ axis - think of it as a sort of rotary 'glide-reflection'; it'll have order $n$ if $n$ is even, or order $2n$ if $n$ is odd.
Dec 21, 2016 at 14:52	history	answered	Bugs Bunny	CC BY-SA 3.0